The image above is an attempt at a recommended bracket using a utility function that minimizes your regret of being wrong. Fan distributions count almost as much as win probabilities with this utility function (which is not peer reviewed). So how much you regret an incorrect pick depends both on the probability of you being wrong (based in win probability) and on the number of other entries likely to get it correct (based on fan distributions). The resulting bracket is mostly robust to the size of your pool (beyond a dozen other entries) and to most common scoring methods.

One of the problems with the utility function used to generate the “which team to pick” widget, is it assumes all you care about is getting the champ right and not having too many other entries also get the champ right. It ignores the possibility of hedging popular picks (eg, Kentucky and Duke), and can recommend some quite improbable champions.

The approach depicted above reflects the mindset of a quantitative portfolio manager. The portfolio manager might choose to minimize his regret of not picking popular picks that turn out to win. He won’t always pick the team most likely to win, because he would really regret being wrong if so many other entrants pick the underdog and the underdog wins. If nobody in your pool picks Northern Iowa, then not picking Northern Iowa either really can’t hurt you.

The traditional NCAA bracket entry is scored in progressive powers of two, such that each round offers 32 points. First round games are worth 1 point, second round 2, etc., and the final game is worth 32.

The leverage of the championship game – worth 32 points out of a possible 192 – is why so many entries pick the overall favorite. This year that favorite will be Kentucky. I predict your pool, if it uses traditional scoring, will have over 40% of the entries picking Kentucky as the champ.

The problem with picking the overall favorite yourself is it is what is known as a “crowded trade.” You already know nearly half the other entries are picking Kentucky. So whether you win the pool, with Kentucky as your champ, is a different matter from whether Kentucky wins the tournament. If Kentucky wins, your pool’s champ will probably be determined by a handful of early round games.

The corollary to this is that if you’re confident in your picking ability, you SHOULD pick Kentucky, because you expect other entries to have worse records than yours in the earlier rounds.

I prefer to look for low hanging fruit in terms of strong teams being underpicked by fans in pools. I predict schools like Virginia, Arizona, Wisconsin, and Villanova will all be underrepresented in pool entries to win it all relative to their probability of winning the whole tournament. Imagine you’re the only one in your pool who picks Wisconsin – that’s a wide margin of error for any earlier round games that you missed. Compare that to if you pick Kentucky – your early round picks had better be nearly perfect.

Scoring method matters. Some pools score rounds in a linearly increasing sequence (1, 2, 3, 4, 5, 6); in this case the final game counts for a mere 6 out of 120 points. Some pools now use Fibonacci (1, 2, 3, 5, 8, 13); here the final is worth only 13 out of 137. In both cases, getting the champ wrong hurts you less than it does in a traditional power-two pool, so you can afford to take more chances.

basketball, March MadnessComments Off on Try the March Madness Fan Simulator widget to decide the champion in your pool entry

Mar192014

This is my perennial warning cautioning against going with the favorite: if you picked Florida as your champ, you probably already lost.

When you think probabilistically about your chance of winning a pool, with no skill your chance is 1/n, where n is the number of entries, including yours.

Given the traditional scoring of 1,2,4,8,16,32, the thinking goes that it behooves you to pick the champion, because that’s where the points are.

While that’s true, the problem with this thinking is you’re competing with all the other bandwagoners who also pick the same favorite. So your chance, with no skill, is no longer 1/n but 1/(1+Florida_picks)*Florida’s chance of winning it all.

Florida’s chance of winning it all ranges somewhere between 13% and 19%, but the percentage of ESPN and Yahoo pool entries that have Florida as the champ range between 29% and 37%.

Assuming Florida does win, whether you win the pool depends on how well you did in Rounds 1-5 versus the other 1/3 of entrants who also picked Florida.

Let’s say you’re in a pool with 24 other participants. Most likely, about 8 of them picked Florida. So your chance of winning is approximately 15%*1/9= 1.67%.

Consider instead (for a 24-person pool) picking Arizona, which has a similar Win Probability but only about 7% of entrants have picked them, or about 2 other entrants in this 24-person pool. Now your chance of winning is 15%*1/3 = 5%.

The math depends on your pool’s scoring, and the right way to do it is a full Monte Carlo simulation that you probably don’t have time for.

The March Madness Fan_Simulator widget might help. It will simulate the top 5 teams you should have picked as Champion given pools of different sizes. This is a scaled down model focused only on the Championship game, but for most pools it that’s good enough. Enter your pool size a few times to watch how the recommended teams change (or not).

Depending on your predictive model, Kansas had somewhere between a 20% and a 25% chance of winning the tournament, and so did Duke. By winning last night, Kansas’ odds didn’t really change much, since they were supposed to beat Lehigh with near certainty, and the same goes for Duke vs. Ar-PB.

Let’s say you’re in a 20-entry pool and 10 have picked Kansas, 2 picked Duke. Ex ante, each Kansas entry has a 2.5% shot at winning, while each Duke pick has a 12.5% shot. Picking Kansas, in effect, was picking the early round upset lottery: if you didn’t get many of yesterday’s upsets, you’re already screwed.